Question

If f(c) = 0, which of the following statements must be true?

A. The point (c,0) lies on the graph of f(x)
B. x - c is a factor of f(x).
C. c is a 0 for f(x).
D. All three statements are true.

Answer 1

"The point (c,0) lies on the graph of f(x)" is the one statement among the following choices given in the question that must be true. The correct option among all the options that are given in the question is the first option or option "A". I hope that this is the answer that has actually come to your help.

Answer 2

The statement that is correct is:

Option: D

D. All three statements are true.

Explanation:

if f(c)=0

• then the value of c so obtained is called the zero of the function f(x).

• Also, if c is a zero then (x-c) is a factor of f(x)

Since, f(x) could be written in the form of : (x-c)g(x)

where g(x) is a function that is the quotient obtained on dividing f(x) by (x-c).

• Also, the point (c,0) lie on the graph of the function f(x)

Hence, all the three given statements are correct.